Principles of the Method of Large Time Increments

1999 ◽  
pp. 55-100
Author(s):  
Pierre Ladevèze
Keyword(s):  
Large Time

Optimal Fault Diagnosis for Networked Control Systems with Large Time-delays and Noises

2012 ◽  
Vol 38 (5) ◽  
pp. 858-864 ◽  
Author(s):  
Juan LI ◽  
You-Gang ZHAO ◽  
Yang YU ◽  
Peng ZHANG ◽  
Hong-Wei GAO
Keyword(s):  
Fault Diagnosis ◽  
Control Systems ◽  
Time Delays ◽  
Large Time ◽  
Networked Control Systems ◽  
Networked Control

scholarly journals Krylov SSP Integrating Factor Runge–Kutta WENO Methods

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1483
Author(s):  
Shanqin Chen
Keyword(s):  
Large Time ◽  
Hyperbolic Equations ◽  
Strong Stability ◽  
Matrix Exponential ◽  
Linear Component ◽  
Nonlinear Hyperbolic Equations ◽  
Time Step ◽  
Integrating Factor ◽  
The Matrix ◽  
Runge Kutta

Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF) methods were designed in the literature, but the methods there were only for one-dimensional (1D) problems that have a stiff linear component and a non-stiff nonlinear component. In this paper, we extend WENO methods with large time-stepping SSP integrating factor Runge–Kutta time discretization to solve general nonlinear two-dimensional (2D) problems by a splitting method. How to evaluate the matrix exponential operator efficiently is a tremendous challenge when we apply IF temporal discretization for PDEs on high spatial dimensions. In this work, the matrix exponential computation is approximated through the Krylov subspace projection method. Numerical examples are shown to demonstrate the accuracy and large time-step size of the present method.

scholarly journals About the Use of Entropy Production for the Landau–Fermi–Dirac Equation

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
R. Alonso ◽  
V. Bagland ◽  
L. Desvillettes ◽  
B. Lods
Keyword(s):  
Dirac Equation ◽  
Classical Limit ◽  
Large Time ◽  
A Priori Estimates ◽  
Landau Equation ◽  
A Priori ◽  
Time Behaviour ◽  
Entropy Dissipation ◽  
Priori Estimates ◽  
Potential Case

AbstractIn this paper, we present new estimates for the entropy dissipation of the Landau–Fermi–Dirac equation (with hard or moderately soft potentials) in terms of a weighted relative Fisher information adapted to this equation. Such estimates are used for studying the large time behaviour of the equation, as well as for providing new a priori estimates (in the soft potential case). An important feature of such estimates is that they are uniform with respect to the quantum parameter. Consequently, the same estimations are recovered for the classical limit, that is the Landau equation.

Time-to-Build and the Inverse U-Shape Investment-Uncertainty Relationship

2008 ◽  
Vol 8 (1) ◽  
Author(s):  
Yishay D. Maoz
Keyword(s):  
Analytical Solution ◽  
Large Time ◽  
Time Lag ◽  
Time To Build ◽  
Small Uncertainty ◽  
Shape Uncertainty ◽  
Uncertainty Relationship

The effect that investment lags have on the uncertainty-investment relationship is studied by modifying the Bar-Ilan and Strange (1996) model to enable an analytical solution. The following results emerge: (i) If the time lag is sufficiently small, uncertainty affects investment negatively; (ii) A sufficiently large time lag gives rise to an inverse U-shape uncertainty-investment relationship; (iii) When such an inverse U-shape exists, the longer the time lag (or the larger the degree of profit convexity), the wider the range of a positive uncertainty-investment relationship.

scholarly journals Global well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

scholarly journals Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 841
Author(s):  
Toshiaki Hishida
Keyword(s):  
Evolution Operator ◽  
Large Time ◽  
Rigid Motion ◽  
Time Dependent ◽  
Energy Relation ◽  
Exterior Domains ◽  
Decay Properties ◽  
Decay Of Solutions ◽  
Whole Space ◽  
Expository Paper

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.

scholarly journals Resolving period aliases for TESS monotransits recovered during the extended mission

2020 ◽  
Vol 500 (4) ◽  
pp. 5088-5097
Author(s):  
Benjamin F Cooke ◽  
Don Pollacco ◽  
David R Anderson ◽  
Daniel Bayliss ◽  
François Bouchy ◽  
...  
Keyword(s):  
Large Time ◽  
Transiting Planets ◽  
Time Period ◽  
Temporal Coverage

ABSTRACT We set out to explore how best to mitigate the number of period aliases for a transiting Transiting Exoplanet Survey Satellite (TESS) system with two identified transits separated by a large time period on the order of years. We simulate a realistic population of doubly transiting planets based on the observing strategy of the TESS primary and extended missions. We next simulate additional observations using photometry (NGTS) and spectroscopy (HARPS and CORALIE) and assess its impact on the period aliases of systems with two TESS transits. We find that TESS will detect around 400 exoplanets that exhibit one transit in each of the primary and extended missions. Based on the temporal coverage, each of these systems will have an average of 38 period aliases. We find that, assuming a combination of NGTS and CORALIE over observing campaigns spanning 50 d, we can find the true alias, and thus solve the period, for up to 207 of these systems with even more being solved if the observing campaigns are extended or we upgrade to HARPS over CORALIE.

Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation

2008 ◽  
Vol 15 (3) ◽  
pp. 531-539
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Large Time Behavior ◽  
Dirichlet Boundary Conditions ◽  
Time Behavior ◽  
Integro Differential Equation ◽  
Homogeneous Data

Abstract Large time behavior of solutions to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. The rate of convergence is given, too. Dirichlet boundary conditions with homogeneous data are considered.

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